1 ( 9 - 8 ) \, - 1 ( 8 - 7 ) \, + 1 ( 7 - 6 ) \, - 1 ( 6 - 5 ) \, + 1 ( 5 - 4 ) is equal to ?

Answer: Option D

Given expression,
$$=\frac{1}{\left(\sqrt{9}-\sqrt{8}\right)}\times \frac{\left(\sqrt{9}+\sqrt{8}\right)}{\left(\sqrt{9}+\sqrt{8}\right)}$$     $$-\frac{1}{\left(\sqrt{8}-\sqrt{7}\right)}$$   $$\times \frac{\left(\sqrt{8}+\sqrt{7}\right)}{\left(\sqrt{8}+\sqrt{7}\right)}$$   $$+\frac{1}{\left(\sqrt{7}-\sqrt{6}\right)}$$   $$\times \frac{\left(\sqrt{7}+\sqrt{6}\right)}{\left(\sqrt{7}+\sqrt{6}\right)}$$   $$-\frac{1}{\left(\sqrt{6}-\sqrt{5}\right)}$$   $$\times \frac{\left(\sqrt{6}+\sqrt{5}\right)}{\left(\sqrt{6}+\sqrt{5}\right)}$$   $$+\frac{1}{\left(\sqrt{5}-\sqrt{4}\right)}$$   $$\times \frac{\left(\sqrt{5}+\sqrt{4}\right)}{\left(\sqrt{5}+\sqrt{4}\right)}$$
$$=\frac{\left(\sqrt{9}+\sqrt{8}\right)}{\left(9-8\right)}-\frac{\left(\sqrt{8}+\sqrt{7}\right)}{\left(8-7\right)}$$     $$+\frac{\left(\sqrt{7}+\sqrt{6}\right)}{\left(7-6\right)}$$   $$-\frac{\left(\sqrt{6}+\sqrt{5}\right)}{\left(6-5\right)}$$   $$+\frac{\left(\sqrt{5}+\sqrt{4}\right)}{\left(5-4\right)}$$
$$=\left(\sqrt{9}+\sqrt{8}\right)-\left(\sqrt{8}+\sqrt{7}\right)$$     $$+\left(\sqrt{7}+\sqrt{6}\right)$$   $$-\left(\sqrt{6}+\sqrt{5}\right)$$   $$+\left(\sqrt{5}+\sqrt{4}\right)$$
$$=\left(\sqrt{9}+\sqrt{4}\right)$$
$$=3+2$$
$$=5$$